text: For shocks in solids, a closed form expression such as equation () cannot be derived from first principles. Instead, experimental observations indicate that a linear relation can be used instead (called the shock Hugoniot in the u-u plane) that has the form
  where c is the bulk speed of sound in the material (in uniaxial compression), s is a parameter (the slope of the shock Hugoniot) obtained from fits to experimental data, and  is the particle velocity inside the compressed region behind the shock front.
  The above relation, when combined with the Hugoniot equations for the conservation of mass and momentum, can be used to determine the shock Hugoniot in the p-v plane, where v is the specific volume (per unit mass):
  Alternative equations of state, such as the Mie–Grüneisen equation of state may also be used instead of the above equation.
  The shock Hugoniot describes the locus of all possible thermodynamic states a material can exist in behind a shock, projected onto a two dimensional state-state plane.  It is therefore a set of equilibrium states and does not specifically represent the path through which a material undergoes transformation.
  Weak shocks are isentropic and that the isentrope represents the path through which the material is loaded from the initial to final states by a compression wave with converging characteristics.  In the case of weak shocks, the Hugoniot will therefore fall directly on the isentrope and can be used directly as the equivalent path.  In the case of a strong shock we can no longer make that simplification directly. However, for engineering calculations, it is deemed that the isentrope is close enough to the Hugoniot that the same assumption can be made.
  If the Hugoniot is approximately the loading path between states for an "equivalent" compression wave, then the jump conditions for the shock loading path can be determined by drawing a straight line between the initial and final states.  This line is called the Rayleigh line and has the following equation: